The aim of this paper is to circumvent this anomaly and restore a bulk-edge correspondence theorem for shallow-water waves, by defining the edge index in a manner which can sample a whole family of boundary conditions at once. We focus on the same family of boundary conditions studied in [1]}, and first show that this provides a (norm-resolvent) continuous parametrization of boundary operators. Then we consider a distinguished loop in the parameter space of longitudinal momentum and boundary conditions (see Figure REF ), and show that it has a well-defined topological index which coincides with the bulk Chern number.
